On a local-global principle for quadratic twists of abelian varieties
Let $A$ and $A^{\prime}$ be abelian varieties defined over a number field $k$ of dimension $g \geq 1$. For $g \leq 3$, we show that the following local-global principle holds: $A$ and $A^{\prime}$ are quadratic twists of each other if and only if, for almost all primes $\mathfrak{p}$ of $k$ of good...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/214506 |
| Acceso en línea: | https://hdl.handle.net/2445/214506 |
| Access Level: | acceso abierto |
| Palabra clave: | Varietats abelianes Geometria algebraica aritmètica Abelian varieties Arithmetical algebraic geometry |
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On a local-global principle for quadratic twists of abelian varietiesFité Naya, FrancescVarietats abelianesGeometria algebraica aritmèticaAbelian varietiesArithmetical algebraic geometryLet $A$ and $A^{\prime}$ be abelian varieties defined over a number field $k$ of dimension $g \geq 1$. For $g \leq 3$, we show that the following local-global principle holds: $A$ and $A^{\prime}$ are quadratic twists of each other if and only if, for almost all primes $\mathfrak{p}$ of $k$ of good reduction for $A$ and $A^{\prime}$, the reductions $A_{\mathfrak{p}}$ and $A_{\mathfrak{p}}^{\prime}$ are quadratic twists of each other. This result is known when $g=1$, in which case it has appeared in works by Kings, Rajan, Ramakrishnan, and Serre. We provide an example that violates this local-global principle in dimension $g=4$.Springer Verlag2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/214506Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1007/s00208-022-02535-0Mathematische Annalen, 2022, vol. 388, p. 769-794https://doi.org/10.1007/s00208-022-02535-0cc-by (c) Francesc Fité Naya, 2022http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2145062026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
On a local-global principle for quadratic twists of abelian varieties |
| title |
On a local-global principle for quadratic twists of abelian varieties |
| spellingShingle |
On a local-global principle for quadratic twists of abelian varieties Fité Naya, Francesc Varietats abelianes Geometria algebraica aritmètica Abelian varieties Arithmetical algebraic geometry |
| title_short |
On a local-global principle for quadratic twists of abelian varieties |
| title_full |
On a local-global principle for quadratic twists of abelian varieties |
| title_fullStr |
On a local-global principle for quadratic twists of abelian varieties |
| title_full_unstemmed |
On a local-global principle for quadratic twists of abelian varieties |
| title_sort |
On a local-global principle for quadratic twists of abelian varieties |
| dc.creator.none.fl_str_mv |
Fité Naya, Francesc |
| author |
Fité Naya, Francesc |
| author_facet |
Fité Naya, Francesc |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Varietats abelianes Geometria algebraica aritmètica Abelian varieties Arithmetical algebraic geometry |
| topic |
Varietats abelianes Geometria algebraica aritmètica Abelian varieties Arithmetical algebraic geometry |
| description |
Let $A$ and $A^{\prime}$ be abelian varieties defined over a number field $k$ of dimension $g \geq 1$. For $g \leq 3$, we show that the following local-global principle holds: $A$ and $A^{\prime}$ are quadratic twists of each other if and only if, for almost all primes $\mathfrak{p}$ of $k$ of good reduction for $A$ and $A^{\prime}$, the reductions $A_{\mathfrak{p}}$ and $A_{\mathfrak{p}}^{\prime}$ are quadratic twists of each other. This result is known when $g=1$, in which case it has appeared in works by Kings, Rajan, Ramakrishnan, and Serre. We provide an example that violates this local-global principle in dimension $g=4$. |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/214506 |
| url |
https://hdl.handle.net/2445/214506 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: https://doi.org/10.1007/s00208-022-02535-0 Mathematische Annalen, 2022, vol. 388, p. 769-794 https://doi.org/10.1007/s00208-022-02535-0 |
| dc.rights.none.fl_str_mv |
cc-by (c) Francesc Fité Naya, 2022 http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
cc-by (c) Francesc Fité Naya, 2022 http://creativecommons.org/licenses/by/3.0/es/ |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Springer Verlag |
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Springer Verlag |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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15,811543 |